words other than "performance" to describe a player's outcome?

There are two potential routes I could recommend in approaching this problem. There are synonyms to performance that you could use, like ability, that would procure a similar effect and make your writing less repetitive. The second route, however, would be to simply become more specific in what ways the player you are trying to describe performed. For instance, if you are a football coach, you could say something about your quarterback like: "this player's quick decision making led to key strategic successes." Small, specific praises will give your players not only a boost to their self-esteem, but a tangible guide to improving as a player.

You might be able to use sport technical expressions like "his shooting accuracy, his goaling score, his ball control skills" or something like that.

I would go with the noun play, which in sports is a commonly-used substitute for performance.

Your examples:

Describing the first player -"his play was outstanding in the previous season".

Describing the second player - "due to his play in the previous season"

As used here, you can think of play as meaning the same thing as quality of play.

From Lexico:

play: the action or manner of engaging in a sport or game.